Problem: Solve for $x$ and $y$ using elimination. ${-4x+2y = -22}$ ${5x-2y = 31}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-4x+2y = -22}\thinspace$ to find $y$ ${-4}{(9)}{ + 2y = -22}$ $-36+2y = -22$ $-36{+36} + 2y = -22{+36}$ $2y = 14$ $\dfrac{2y}{{2}} = \dfrac{14}{{2}}$ ${y = 7}$ You can also plug ${x = 9}$ into $\thinspace {5x-2y = 31}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ - 2y = 31}$ ${y = 7}$